Carson bandwidth rule

In telecommunications, the Carson's bandwidth rule defines the approximate bandwidth requirements of communications system components for a carrier signal that is frequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency. Carson's rule does not apply well when the modulating signal contains discontinuities, such as a square wave. Carson's rule originates from John Renshaw Carson's 1922 paper.

Carson's bandwidth rule is expressed by the relation: $$\mathrm{C}\mathrm{B}\mathrm{R}=2(\mathrm{\Delta }f+f_m)$$ where:

• $\mathrm{C}\mathrm{B}\mathrm{R}$ is the bandwidth requirement;
• $\mathrm{\Delta }f$ is the peak frequency deviation; and
• $f_{\mathrm{m}}$ is the highest frequency in the modulating signal.

For example, a typical VHF/UHF two-way radio signal using FM mode, with Template:Val peak deviation, and a maximum audio frequency of Template:Val, would require an approximate bandwidth of Template:Nowrap Template:Val.

Standard broadcast stereo FM, with a peak deviation of Template:Val, has a highest modulating frequency (which combines Template:Nowrap and Template:Nowrap) of Template:Val (assuming no RDS or other subcarriers). Most of the energy therefore falls within an approximate bandwidth of Template:Nowrap Template:Val. (Geographically close FM broadcast transmitters are almost always assigned nominal center frequencies at least Template:Val apart).

Carson's bandwidth rule is often applied to transmitters, antennas, optical sources, receivers, photodetectors, and other communications system components.

Any frequency modulated signal will have an Template:Em number of sidebands and hence an infinite bandwidth but, in practice, all significant sideband energy (98% or more) is concentrated within the bandwidth defined by Carson's rule. It is a useful approximation, but setting the arbitrary definition of occupied bandwidth at 98% of the power still means that the power outside the band is about $10\log \left(\frac{0.98}{0.02}\right)\approx$ $17\mathrm{d}\mathrm{B}$ less than the carrier inside, therefore more information is needed for spectrum planning.Template:Cn

References

• Template:FS1037C
• Leon W. Couch II, "Digital and Analog Communication Systems, 6th Edition", Prentice-Hall, Inc., 2001. Template:ISBN